Close transposition but want to avoid dissonance

Question

So I had this idea to have a march in canon. So I would have a rhythmic cell like this:

to give a march-like feeling. I have decided on 6 rhythmic cells before a note change and going up 1 note and then down the entire major scale. To make this not seem boring, I decided on having the march in canon with 3 lines(second line comes in halfway through first line, third line comes in halfway through second line). I also decided to have a close transposition, to make it sound like there are chords being played. So I tried starting with a 3rd transposition. But this lead to there being a second between 2 notes which was repeated. I figured this was too dissonant, even though I usually think of the most dissonant interval as being a tritone. So then I tried a 4th transposition and it sounded beautiful, with only 2 dissonant intervals, both being tritones.

Adding a transposition by a third on top of that meant many more tritones, diminished chords, incomplete 7th chords, sus chords, and probably some chords that you could only describe by the details of the intervals. But I was wanting it to sound like chords, just not with a lot of dissonance. I got second inversion C minor chords this way and of course, the ending tonic major chord. But those are about the only consonant chords I got.

But would a transposition by a 5th for both lines, which would ensure consonance be considered close? I don't think so because then you have basically power chords throughout. Transposition by a fourth over another transposition by a fourth would give a lot more sus chords in second inversion, a jazzy chord. Not what I was aiming for either. So if this won't work, will I have to adjust transposition chord by chord to make it sound like major and minor chords(which is what I was aiming for, not dissonance or a jazzy sound).

This march in canon idea is really an idea for a theme in a symphony related to war. I figured that if I could put a symphony to words, it would be easier to write and not so overwhelming.

So how can I have a close transposition in all the lines while also ensuring consonance with maybe a few 7th chords or diminished chords where I get those tritones in the first 2 lines?

Answer 1

(A fair warning before I start: I'm wondering if it's even mathematically possible for you to have to a strict canon, using only particular intervals, with the harmonic stipulations that you're looking for. This is a pretty advanced outcome using such basic musical input; it's a bit like fighting a nuclear war with only revolutionary-war era materials. But whether such an outcome exists or not, I think your composition of this canon will largely be a trial-and-error scenario.)

Whenever you write a canon, you want to write the voices together to prevent yourself from painting yourself into a corner.

You can simplify the process by first considering just a two-voice canon. You have the first voice, the dux, and the second voice, the comes. To start off, just test different intervals of canon and how that relates to your scale:

C D E F G A B C B A G F E D C
      D E F G A B C D C B A G F E D
      3 3 3 3 3 1 3 5 5 5 5 5

Doing this gives us a sense of the intervals that are created by just two voices when we have a canon at the second. You can then try other intervals (both time and pitch intervals) and adding in other voices to see what intervals emerge. Here, for instance, is the outcome if we add a third voice using the exact stipulation from above:

C D E F G A B C B A G F E D C
      D E F G A B C D C B A G F E D
            E F G A B C D E D
      3 3 3 M M 3 3 M 5 * $ $

(* is a m7 without a third, and $ is a sus2 chord.)

But what's important is that, whatever the first interval created is, you're going to have a lot of those until the scale goes back down. Because of this, I worry that your harmonic outcome is going to be much more limited than you're hoping for.